Is it possible to make light pass through only a part of the texture
You can use a mix shader connected to a transparency and diffuse nodes, the texture is the one that controls the mix:



Then just use volume scattering in the world volume.

Usually the default density for volume scatter is way to high, so play with the values until you find the right one for your needs.

keep in mind also that the emitter object inside might need to be quite bright.